Question

question 16 (4 points) solve the following system graphically or algebraically. upload your handwritten work displaying how you solved or upload a screenshot of desmos with your answers for credit. \

$$\begin{cases} y = x^2 - 4x + 4 \\\\ y = x - 2 \\end{cases}$$

Explanation:

Step1: Set equations equal

Since both equal $y$, set them to each other:
$x^2 - 4x + 4 = x - 2$

Step2: Rearrange to quadratic form

Move all terms to left side:
$x^2 - 4x + 4 - x + 2 = 0$
$x^2 - 5x + 6 = 0$

Step3: Factor the quadratic

Factor the trinomial:
$(x-2)(x-3) = 0$

Step4: Solve for $x$

Set each factor to 0:
$x-2=0 \implies x=2$
$x-3=0 \implies x=3$

Step5: Find corresponding $y$

Substitute $x$ into $y=x-2$:
For $x=2$: $y=2-2=0$
For $x=3$: $y=3-2=1$

Answer:

The solutions are $(2, 0)$ and $(3, 1)$